Mathematical Analysis of an Ideal ZED

[mondrasek]

Why would you want to do that?

Because that would mean the E_in needed to bring a second ZED from State 1x to State 2 would be reduced by 0.5*0.202454mJ I think.

[MarkE]

MarkE,

Are you saying that I can ALWAYS vent the fluid out of the pod chamber and have the system return to state 1?

If you open the valve at the bottom of the pod chamber you change the thing into a glorified crazy straw.  In any state, the force that reflects back to the pod chamber is the sum of the relative areas times the heads as previously shown in LarryC's 0+3+3, and 1+2+4 model.  When there is water in the pod chamber, this is like his 1+2+4 and there is net force required to hold the water in the pod chamber.  Heads in odd AR#'s add to the reflected force, heads in the even AR#'s subtract and there are additional terms due to the nested risers.  The thing will drain so long as the reflected sums of the other annular ring forces and the weight in the pod chamber is positive.  Once the machine has been set-up to State 1 with the associated venting, the neutral condition is State 1X not State 1.   You can play with the spreadsheet and see if that's what you get.

[MarkE]

Because that would mean the E_in needed to bring a second ZED from State 1x to State 2 would be reduced by 0.5*0.202454mJ I think.

You can change the conditions, and you can change the states, but what you can't do is find any combination that will give you a closed cycle with an energy gain over that cycle.  Adding complexity only worsens the situation.

[MarkE]

I am a little confused.  If I can pull the plug on the pod chamber and it will fall apart and go back to state 1,, will it be able to do it with these settings.

Why do you ignore what I write? 

The thing will drain so long as the reflected sums of the other annular ring forces and the weight in the pod chamber is positive.  Once the machine has been set-up to State 1 with the associated venting, the neutral condition is State 1X not State 1.   You can play with the spreadsheet and see if that's what you get.

What is confusing you? You've entered drastically different dimensions, so now State 1X is a higher energy state than State 3.  There should be no big surprise that the system will not have a tendency to go from State 3 to State 1X for those conditions.

Click on the cell number and enter these values

B27 RiserWallThickness   257.5

Are you making bank vaults?  10" wide riser walls???

B28 RingWallThickness    0.25
B29 PodOD                400
B30 PodHeight           4000
B31 ST1_PrefillHeight   3000
B111 ST2_AR1Height      2000

This setup leaves lots of room for any further movement of the air\water columns and has no over or under issues with the columns and volumes.

I arranged these numbers to make it easy for me to see so you will not see them all together like this in the spreadsheet.

Input                   89.4066834062J

Would you be so kind as to either refer to cell #'s or use the actual names in the spreadsheet?  This value is ST2_EnergyAdded  the total energy in state 2 for your conditions:  ST2_EnergyAddedPlusST1E = 1070.4582073J

Output                 289.5823115248J

This is cell ST2_ST3_External_Work_Performed.

Input to Output        325.07%   

This is cell ST2_ST3_PCT_ENERGY_LOSS vs ST2_ENERGY_ADDED.  There should be no big surprise since you made made the risers gigantic there is now lots more energy stored in State 1, and State 1X than incrementally added going to State 2. 

      
Uplift distance          4.4593613399mm
Total uplift force  130348.603561497N

State 1 Energy         981.0515238844J
State 2 Energy        1070.4582072907J
State 3 Energy         779.8224455746J

Again, what is surprising to you here?  And why is it that you choose to pick cells an internal energy change and label that as OUTPUT? B225 is clearly named as: ST2_ST3_ENERGY_LOSS.  B226 is clearly named as: ST2_ST3_External_Work_Performed.  In your set-up, ST2_ST3_ENERGY_LOSS = 290.6357617J while ST2_ST3_External_Work_Performed = 289.5823115J.  The spreadsheet continues to demonstrate the inherently lossy behavior even with your bank vault riser walls.

[MarkE]

This is my modified file.

I took MarkE's file and removed the graphics and then down at the bottom of state 3 I added some things so you can change the dimensions,, I pointed the actual cells up above to these cells, and I included the height levels so you can see those changes,, no red numbers are allowed,, that would be blowing something

I am sure MarkE would do a much better job of it,, I am not a spreadsheet person.

Since all the formula references are to named cells you could have just cut and pasted the lines you wanted to group together.  For some reason you renamed many cells with a _1 suffix.  It looks like you left the form of the calculations intact.  So you should still be getting the right answers.  What you label as Input at B230 is:  ST2_EnergyAdded_1 (_1 your relabel) and what you label as Output is:  ST2_ST3_External_Work_Performed_1 (_1 your relabel).  The real "input" is the internal energy lost in the cell immediately above:  ST2_ST3_ENERGY_LOSS_1 (_1 your relabel).  As you relabeled that cell, I think you should be aware of it.